An illusory correlation occurs when two variables are significantly correlated - increases in one variable tend to co-occur with increases (or decreases) in the other variable - but changes in one variable do not cause changes in the other variable.

Often times, illusory correlations between two variables are the result of a third-variable problem - a secret, unmeasured third variable causes reliable changes in bothvariables. For example, the number of horses owned throughout life is significantly correlated with lifespan. This is a real, significant correlation, but does it mean that owning a horse causes a person to live longer? Or, alternatively, is there a secret third variable that causes both variables to rise. Think about it - what is the third variable? ... Wealthis the secret third variable that causes increased number of horses owned and increased lifespan!

1. What is a third-variable problem?

2. Howcan a third-variable problem create an illusory correlation?

3. Name a potential third-variable cause for the correlations below. Explain your reasoning.

a. The more air conditioners are sold in a day, the more drownings tend to occur that day.

b. Countries with more butter have happier citizens.

c. Children who start text-messaging at a younger age test higher in reading ability.

d. More time spent on social media is related to lower grades in college.

e. Towns with more churches per square mile tend to have a higher crime rate.

f. Increased flossing is related to longer lifespan.

g. Eating unhealthy food during childhood is correlated with prison time in adulthood.

h. Among teens, listening to music with sexual lyrics is correlated with sexual activity.